Physics - 203 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Elastic Behavior of Lead Germanate Near Transition Temperature I. J. Abdul Ghani Department of Physics, College of Education Ibn Al-Haitham, University of Baghdad Receired in:15 April 2012 Accepted in: 9December 2012 Abstract All the stiffened and unstiffened elastic constants for lead germanate (Pb5Ge3O11) single crystal have been measured from room temperature 298 K up to 513K by using ultrasonic pulse superposition technique. The correction of piezoelectric stiffening has been used to obtain the unstiffened elastic constants. Elastic moduli of lead germanate (C11, C33, C12, C13, C44 and C66) decrease with the increase of temperature. C11, C33, C12 and C13 suffered a dip at transition temperature but they increase with the increase of temperature just above Curie temperature between 453 and 473 K because of their positive temperature coefficients in this range, and then decrease slightly (except C12 increases) in the range between 473K and 513K. But for the shear elastic moduli (C44 and C66): C44 shows very slight and gradual increase and then decrease with the increase of temperature, while C66 shows a small and graduate decrease with increasing temperature. These measurements were compared with previous experimental published work. Keywords: Lead germanate, Elasticity, Phase transition, Optical activity, Piezoelectric crystal Introduction Lead germanate single crystal (Pb5Ge3O11) is both ferroelectric [1,2] and optically active below Curie temperature Tc = 450 K [3-5]. In several biaxial ferroelectrics optical activity has been observed, but is the only uniaxial ferroelectric studied in detail. Lead germinate undergoes ferroelectric phase transition with emerging of spontaneous polarization along the unique trigonal [6]. Lead germanate single crystal is ambidextrous; [7] below Curie point (450 K) the handedness of the optical activity inverse when the spontaneous polarization is reversed by an applied electric field. Both the optical activity and the spontaneous electric polarization disappear at the Curie temperature [8,9]. At Tc = 450 K lead germanate undergoes a second order phase transition from the paraelectric to the ferroelectric phase [5,9] which gives rise to very rapid changes of polarization P with temperature just below Tc. The Curie temperature decreases toward room temperature with uniaxial pressure [10] and doping of germanium in Pb5Ge3O11 by Si or Ba [11,12]. Measurements of polarization as a function of temperature confirmed the shift in the transition temperature [11]. Lead germanate is not of interest as an acousto-optic material [13] or as a transducer since electromechanical coupling factors are small [14] and ultrasonic attenuation is large [13] but the electro-optic coefficients shows more promise [15,16]. By applying resonance technique Yamada et al. [14] have measured the values of all elastic, dielectric and piezoelectric constants at room temperature, as well as the temperature dependence of the elastic compliance S11E and of the two piezoelectric constants d31 and d22. Both S11E and d31 show upward directed cusp-like anomalies near Tc, but d22 is approximately independent of temperature [14]. Both in the ferroelectric and in the paraelectric phases, the Physics - 204 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 dielectric constant ε33 follows a Curie-Weiss law [2,17], but ε11 is only weakly temperature dependence. Several soft Raman active modes have been observed [18,19] which decrease with temperature in a manner so as to lead Lyddane-Sachs-Teller relation via to the Curie- Weiss law for ε33 [17]. Second order elastic constants (SOEC) of lead germanate single crystal at room temperature have been calculated [14,20]. The purpose of this work is to report experimental data on all elastic constants (stiffened and unstiffened) versus temperatures from room temperature 298 to 513 K, and to compare the results with previous published work of Barsch et al. [21]. At room temperature Pb5Ge3O11 belongs to the R3 ̄ ̄̄̄ Laue group, crystals of which have a more complicated elastic behavior than those belonging to the higher symmetry R3¯m Laue group. There are seven independent elastic moduli: C11, C33, C44, C12, C13, C14 and C25. The point symmetry changes to 6¯= 3/m (C3h) at phase transition, decreasing the number of independent elastic constants from seven to five: C11, C33, C44, C12, and C13 [21]. Above Curie point, C14 and C25 are zero. In ferroelectric state (below Curie temperature) lead germanate crystals contain 180o domains. In this work unpoled crystals were used which twinned on a very fine scale too small to be seen optical. Because of twining, the effective symmetry is 6¯, rather than 3, so that the elastic constants C14 and C25 are absent in unpoled lead germanate, both above and below the transition temperature. Because C14 and C25 are very small, it makes very little difference whether measurements are made on single-domain specimens or not. Room temperature measurements on single-domain Pb5Ge3O11 gave C14 = 0.004x1010 N.m–2 and C25 = 0.00, more than twenty times smaller than the other five elastic constants [20]. Till today, very limited experimental data are available in literature on the measurements of the elastic constants of lead germanate at different temperatures, due to the complicated and unique structure of this crystal; its structure changes from ferroelectric rhombohedral below Curie temperature to paraelectric hexagonal above Curie temperature. Experimental procedure Good optical-quality large single crystalline boules of Pb5Ge3O11 grown by Czochralski method, and well-characterized growth defect [22] with density value of 7390 kg.m-3. Platelets of the crystal about 3 to 5 mm thick with orientations in [100], [001] and in direction of 45o to these crystallographic axes were prepared. For ultrasonic measurements, gold plated quartz transducers X (longitudinal) and Y (shear) cut transducers with resonance frequency of 10 MHz and with diameters of 6 mm and 4 mm have been used [23] were cemented to specimen with non-aqueous stopcock grease and also phenyl salicaylate have been found to be suitable for bonding at room temperature, but above 473 K (Extempt 9901 lubrication Engineering Co.) is superior as a bond material. A pulse echo overlap system is used to measure the ultrasonic wave transit time [21,23,24] the travel times of 20 MHz longitudinal and transverse waves were measured for eight different modes at 5 deg intervals from 323 to 523 K, except near transition temperature where data were taken in 1 deg increments. In the vicinity of the transition ultrasonic attenuation was found to increase considerably. Errors from thermal gradients and temperature measurements were smaller than 0.3 deg. Results In Table 1, the relations for the stiffened elastic constants Cµv´ = ρV2 (V is actual ultrasonic velocity, and ρ is a density of the crystal), in terms of the unstiffened constants CµvE and the piezoelectric correction as obtained from eign values of the Christoffel tensor with the piezoelectric contributions included [25] are listed for eight modes measured. The relations Physics - 205 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 for ρVi2 were obtained from the general relations for C3 symmetry by taking into account that for lead germanate the piezoelectric constants e11 = e14 = 0 [14] and by averaging over two domain states. Since the domains differ in the direction of the polar C-axis, the piezoelectric constants e14, e15, e13 and e33 (but not e11 and e22) are of opposite sign in the two types of domains. For the modes i = 6, 7 and 8 the relation for ρVi2 in Table 1 are only accurate up to and including fourth power of the piezoelectric constants. In Table 2 the present experimental values of stiffened and unstiffend elastic constants of lead germanate at different temperatures (298, 323, 348, 373, 398, 423, 448, 473 and 513 K) calculated using the equations of ρVi2 from Table 1 and compared with Barsch et al. [21] values. Thermal expansion data required for calculating the density and ultrasonic path length versus temperature were taken from Iwasaki et al. [12]. Measurements are referred to right-handed orthogonal axes X1, X2 and X3 parallel to crystallographic directions [100], [120] and [001]. Hexagonal materials are transversely degenerate so that all directions in [001] are equivalent. In Fig. 1 both the stiffened elastic constants Cµv´ (calculated by ignoring the piezoelectric correction terms in Table 1) and the unstiffened elastic constants CµvE (after subtraction of piezoelectric stiffening) listed in Table 2 are plotted as a function of temperature using pulse superposition technique and compared with Barsch et al. results [21] using the same technique. The longitudinal moduli C11 and C33 were obtained from modes number 1, 4 and 7 plus 8, the shear moduli C44 and C66 are calculated from modes 3 and 5, and from modes 2 and 6, respectively. The off-diagonal modulus C12 was obtained from C66 = (C11–C12)/2 and C13 from modes 7 and 8. The dielectric constant data required for the evaluation of the piezoelectric correction terms were obtained by extrapolating the measurements of Cline and Cross [17] on the frequency dependence of ε33 to 20 MHz. Room temperature piezoelectric constants as determined by Yamada et al. [14] are e11 = 0.00, e14 = 0.00, e15 = 0.08, e22 = 0.09, e31 = 0.61 and e33 = 0.77 C.m–2. Since the only piezoelectric constants for which the temperature dependence has been measured are d31 and d22, and since d22 is practically independent of temperature [14], it was assume that at all temperatures e31 = e33, and that all other piezoelectric moduli are temperature dependence. The modulus e = e31 = e33 was then determined from d31 by means of the relation e = d31 / (S11E + S12E + S13E), where e and elastic compliances S11E, S12E and S13E were determined [14] self-consistently by interaction of the equations given in Table 1. Since the room temperature value of e obtained in this manner (0.158 C.m–2) is smaller than e31 and e33 of Yamada et al. [14]. All values of e were then multiplied by constant factor so as to bring the room temperature value into agreement with the average value (e31 + e33)/2 calculated from the values of Yamada et al. [14]. The dielectric constant data calculated from Uchida et al. [15] and the piezoelectric constants obtained in the manner outlined are listed in Table 3. The elastic constants plotted in Fig. 1 as a function of temperature for unpoled lead germanate showed downward directed cusp-like anomalies for the moduli C11, C33, C12 and C13, and a continuous monotonically decrease with the increase of temperature for the shear moduli C44 and C66 = (C11–C12)/2. For C33 and C13, the piezoelectric correction is large, so that the magnitude of the elastic anomalies is larger for unstiffened constants than stiffened ones. Since in the paraelectric phase the piezoelectric constant d31 is zero [14] the difference between the stiffened and unstiffened moduli should be negligibly small above the transition. At room temperature, the uncertainty of the data arising from inconsistencies in the different modes and from errors in density and ultrasonic path length, and from piezoelectric correction amount to about 0.5 to 1%. Above room temperature the errors should not be significantly larger for C11, C12, C44 and C66 in the ferroelectric phase. Because of the unknown error of d31 used in the piezoelectric correction, and especially because of the simplifying assumption e31 = e33 underlying the estimate of the piezoelectric correction term, the errors of C13E and C33E in the ferroelectric phase should be larger than the errors for other Physics - 206 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 moduli, and they may be expected to increase with the increase the temperature up to Curie point. Discussion The shape of the curves for the temperature dependence of the elastic moduli in Fig.1 suggests decomposing the moduli CµvE additively into the usual linearly temperature dependence term Cµvo = aµv – bµv T and into the cusp-like elastic anomaly ∆Cµv as given by: CµvE = Cµvo + ∆Cµv (1) Since it is apparent from Fig. 1 that the shear modulus C66 = (C11–C12)/2 does not exhibit an elastic anomaly, which shows good agreement with Barsch et al. [21] results. It follows that both in the ferroelectric and in the paraelectric phases the following relation holds: ∆C11 = ∆C12, (2-1) Further one obtains from graphical analysis of the data in Fig.1 that the relationship: ∆C11 ∆C33 = (∆C13)2 (2-2) holds approximately in ferroelectric phase, but not in the paraelectric phases. The relative error of the ∆Cµv shows similar temperature dependence, because the absolute error of the piezoelectric correction increases with the increase of temperature. This suggests that the deviations of the ∆Cµv from Eq. (2-2) are primarily caused by systematic errors of the ∆Cµv. Furthermore, C44 does not show an elastic anomaly, thus it is: ∆C44 = 0 (2-3) In both the ferroelectric and the paraelectric phases which show a good agreement with Barsch et al. results [21]. Barsch et al. [21] discussed in full detailed the reasons of elastic anomalies of lead germinate single crystal for both the ferroelectric phase (C13) and the paraelectric phase (C3h). The elastic anomaly in lead germanate could arise from a soft Raman active mode through the internal strain contributions of the elastic constants. All the Raman-active modes occur at the Brillouin zone center and so lead to displacive ferroelectric phase transition [18]. Miller and Axe [26] found that the elastic anomaly in β-quartz (space group D16 or D56) obeys the three Eqs. (2-1), (2-2) and (2-3), with regular terms Cµvo taken as constants. They showed that the elastic anomaly in β-quartz could arise from a soft Raman active mode through the internal strain contributions of the elastic constants. Axe and Shirane [27] have later established that the elastic anomaly in β-quartz could no longer be attributed to the internal strain contributions. They showed that the anharmonic contribution arising from virtual excitation of optical phonon pairs of wave vector q and –q of an over damped soft mode could lead to elastic anomaly of the Eqs. (2-1), (2-2) and (2-3) if q is along the crystallographic C-direction [27]. Although the explanation of the elastic anomaly originally proposed by Miller and Axe [27] is not relevant for β-quartz it appears that the internal strain mechanism could account for the elastic anomaly in lead germinate. Viswanathan [28] found that the gyrotropic anomaly in Pb5Ge3O11 during phase transition lead to elastic anomalies on C11, C33, C12, and C13 which suffered a dip at the transition temperature which show agreement with the present results and with Barsch et al. [21] results. In ferroelectric phase the elastic anomaly for lead germanate obeys the three relations (2-1), (2-2) and (2-3), and since the lowest of the optical modes are soft and strongly temperature dependent [18,19], it is very likely that the elastic anomaly arise predominantly from soft mode through the internal strain mechanism. Barsch et al. [21] found that Pb5Ge3O11 was the first material for which the linear acoustic–optic mode coupling mechanism proposed by Miller and Axe [26] is operative. Harmonic phonon-phonon interactions may also contribute to the elastic anomaly. Physics - 207 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Generally, elastic moduli decrease with the increase of temperature, at least one of the coefficients must increase with temperature to achieve temperature compensation. Most materials soften at higher temperatures; the few with positive temperature coefficients generally show phase transition of some sort. Several of the elastic constants of Pb5Ge3O11 increase with the increase of temperature just above Curie point between 453 and 473 K. C11, C33, C12 and C13 have positive temperature coefficients in this range. Since the Curie point of Pb5Ge3O11 can be lowered to room temperature by doping the crystal by Si or Ba, the temperature compensation region can be moved to a more convenient working range. Unfortunately the 20 deg range of positive temperature coefficients is rather narrow and stiffnesses are changing rather rapidly. The piezoelectric coupling coefficients of lead germanate are also rather small for surface-wave devices [14], and losses tend to be high [13]. Thus it appears that the advantages of positive temperature coefficients to several elastic moduli are more than offset by other factors, and lead germinate, would be of little use as substrate material for ultrasonic surface wave devices. The discrepancies range for unstiffefend elastic constant at different temperatures for this work comparing with Barsch et al. results [21] are from 1% for C33 and 5.3% for C13. Conclusions From the present results, it can be concluded that the unpoled lead germanate showes an elastic anomalies for the elastic moduli C11, C33, C12 and C13 and a small continuous monotonically decrease for the shear moduli C44 and C66 with the increase of temperature. Several of the elastic constants of Pb5Ge3O11 increase with the increase of temperature just above Curie point. The elastic anomalies for unstiffened elastic constants CE33 and CE13 are larger than the stiffened elastic constants C´33 and C´13 because the piezoelectric correction is large. Above Curie temperature (450 K) the difference between the stiffened and unstiffened elastic constants was small above transition temperature. The measured present results agreed with the previous results of Barsch et al. [21]. Acknowledgements I am so grateful to Professor G.A. Saunders for many helpful discussions and much encouragement of this project. References 1. Iwasaki, H.; Sugi, K.; Yamada, T. and Niizeki, N. (1971), 5PbO.3GeO2; A new ferroelectric, Appl. Phys. Lett.18 (10): 444-445. 2. Nanamatsu, S.;Sugiyama, S.; Doi ,K. and Kondo, Y. (1971), Ferroelectricity Pb5Ge3O11, J. phys. Soc, Japan, 31:616-620. 3. Iwasaki, H. and Sugii, K. (1971), Optical Activity of Ferroelectric 5PbO.3GeO2 Single crystal, Appl. Phys lett,19( 4): 92-93. 4. Mendricks, S.;Yue ,X.; Pankrath, R. and Hesse ,H., Kip D., (1999), Dynamic Properties of Multiple Grating Formation in Doped and Thermally Treated Lead Germanate, Appl. Phys. B68, 887-891. 5. Yue, X.; Mandricks, S.; Yi Hu, Hesse H. and Ki, D. (1998), Photorefractive Effect in Doped Pb5Ge3O11 and in (Pb1-xBax)5Ge3O11, J. Appl. Phys. 83 (7): 3473-3479. 6. Trubitsyn, M.P.; Volnianskii ,M.D., Ermakov A.S., and Linnik V.G, (1999), Ferroelictric Phase Transition in Lead Germanate Pb5Ge3O11 Studied by ESR of Cd+3 Prope, Condensed Matter Phys.2 (4):677-684. 7. Newnham, R.E. and Gross, L.E. (1974), Ambidextrous Crystals, Endeavour 23, 18-23. Physics - 208 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 8. Shaldin, Yu.V., Bush A.A., Matyjasik S., and Rabadanov M.Kh., (2005), Characteristic of Spontaneous Polarization in Pb5Ge3O11 Crystals, Crystallography Reports 50 (5): 836- 842. 9. Mirsa, N.K.; Sati, R. and Choudhary, R.N.P. (1996), Phase Transition in Modified Lead Germanate , Ferroelectrics, 189 1, 39-42. 10. Molak, A.; Koralewski, M.; Saunders, G.A. and Juszczyk, W. (2005), Effect of Uniaxial Pressure on the Ferroelectric Phase Transition in Pb5Ge3O11: Ba Crystal, Acta Phys. Pol. A 108 (3): 513-520. 11. Nanda Gowswami, M.L.; Choudhary, R.N.P. and Mahapatra, P.K.,(1999), Ferroelectric Phase Transition in Modified Lead Germanate, Ferroelectrics 227( 1): 175-187. 12. Iwasaki ,H.; Miyazawa, S.; Koizumi ,H.; Sugii ,K. and Niizeki, N. J. (1972), Ferroelectric and Optical Properties of Pb5Ge3O11 and its Amorphous Compound Pb5Ge2SiO11, Appl. Phys. 43(12): 4907-4915. 13. Ohmachi, Y. and Uchida,N. J. (1972), Acousto- Optic Properties of Single Crystal 5PbO.3GeO2, Appl. Phys.43, 3583-3584. 14. Yamada, T.; Iwasaki ,H. and Niizeki, N., J. (1972), Elastic and Piezoelectric Properties of Ferroelectric 5PbO.3GeO2 Crystals, Appl. Phys. 433, 771-775. 15. Uchida, N.; Saku, T.; Iwasaki H., and Onuki K., J. (1972), Electro-Optic Properties of Ferroelectric 5PbO.3GeO2 Single Crystal, Appl. Phys. 43 (12): 4933-4936. 16. Bichard, V.M.; Davies, P.H.; Hulme, K.F.; Jones, G.R. and Robertson, D.S., (1972), Electro-Optic Measurements on Lithium Germanate (Li2O.GeO2) and Lead Germanate Pb5Ge3O11, J. Phys. D Appl. Phys. 5 (11): 2124-2128. 17. Cross, L.E. and Cline, T.W., (1976), Contribution to the Dielectric Response from Charged Domain Walls in Ferroelectric Pb5Ge3O11, Ferroelectrics 11, 333-336. 18. Ryan, J.F. and Hisano, K. (1973), Raman Scattering and Ferroelectric Phase Transition in 5PbO.3GeO2, J. Phys. C. Solid State Phys. 6, 566-574. 19. Burns, G.and Scott, B.A. (1972), Soft Optic Phonon Mode in Ferroelectric Pb5Ge3O11, Phys. Lett. A 39, 177-179. 20. AlMummar, I.J.; Saunders, G.A. (1986), Acoustic Symmetry and Vibrational Anharmonicity of Rhombohedral Pb5Ge3O11 and Pb4.7Ba0.3Ge3O11, Phys. Rev. B 34( 6): 4304-4315. 21. Barsch, G.R.;Bonczar, L.J. and Newnham, R.E. (1975), Elastic Constants of Pb5Ge3O11 from 25 to 2400C , Phys. Stat. Sol. A 29, 241-250. 22. Sugii, K.; Iwasaki, H. and Migazawa, S. (1971), Crystal Growth and Some Properties of 5PbO.3GeO2 Single Crystals, Mater Res. Bull.6, 503-512. 23. Al-Mummar, I.J. (1985), Ultrasonic Studies of the Elastic Properties of Lead Germanate Under Pressure, M.Sc. Thesis, Bath University, Bath, UK. 24. Mc Skimin, H.J. (1961), Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in Solids, J. Acoust. Soc. Am. 33 1, 12-16. 25. Kyame, J.J. (1949), Wave Propagation in Piezoelectric Crystals, J. Acous. Soc. Am.21, 159-167. 26. Miller, P.B. and Axe ,J.D. (1967), Study of Optical and Elastic Properties of α-β Quartz, Phys. Rev.163, 924-929. 27. Axe, J.D. and Shirane, G. (1970), Study of the α-β Quartz Phase Transformation by Inelastic Neutron Scattering, Phys. Rev. B1, 342-348. 28. Viswanathan, K.S. (1994), Elastic and Gyrotropic Anomalies and Acoustic Activity in Lead Germanate, Can. J. Phys. 72 9-10, 568-573. Physics - 209 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Table( 1): Relation between ultrasonic velocities (Vi), stiffened elastic constants (Cµv´), and unstiffened elastic constants (CµvE). Mode i Direction of ρVi2 Propagation Polarization 1 X1 X1 C11E 2 X1 X2 C66´ = C66E + e222/ε11S 3 X1 X3 C44´ = C44E + e152/ε11S 4 X3 X3 C33´= C33E + e332/ε33S 5 X3 X1 C44E 6 45o to X1, X3 X2 2 (C44E + C66E) + V2 – ∆ 7 45o to X1, X3 Quasi longitudinal [A + (B2 + 4C)1/2 ]/4 8 45o to X1, X3 Quasi shear [A − (B2 + 4C)1/2 ]/4 A = (C11E + C33E + 2C44E) + 2(U2 +V2 + W2) + 2∆ B = (C11E − C33E − 2C66E) + 2(U2 –V2 + W2) − 2∆C C = − (C11E + C66E +2U2) (C33E– C66E – 2V2 + 2W2) + (C13E + C44E +2VW) 2 +4V2 (V2+ W2) ∆ = 2V2 [(C11E − C66E +2U2) W2 + (C33E – C66E – 2V2 + 2W2) V2 – 2(C13E + C44E + 2VW) VW] / [(C11E − C66E +2U2) (C33E – C66E – 2V2 + 2W2) – (C13E + C44E + 2VW) 2] U2 = 2(e22)2 / (ε11S + ε33S) V2 = (e15 + e31)2 / 2(ε11S + ε33S), W2 = (2e15 + e33)2 / 2(ε11S + ε33S) Physics - 210 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Table 2. Experimental values of stiffened elastic constants (Cµv´) and unstiffened elastic constants (CµvE) in 1010 N/m2 at different temperatures (calculated from ρVi2 in Table 1). T (K) C11E C11´ C12E C12´ C13E C13´ C33E C33´ C44E C44´ C66E C66´ 298 6.78* 6.78* 2.52* 2.50* 1.79* 1.92* 9.30* 9.43* 2.24* 2.20* 2.13* 2.14* 6.80† – 2.57† – 1.89† – 9.42† 9.55† 2.23† 2.21† 2.11† 2.12† 323 6.72* 6.72* 2.48* 2.47* 1.77* 1.90* 9.24* 9.40* 2.24* 2.20* 2.12* 2.13* 6.75† – 2.55† – 1.87† – 9.35† – 2.23† – 2.10† – 348 6.67* 6.67* 2.46* 2.45* 1.75* 1.89* 9.18* 9.38* 2.23* 2.195* 2.11* 2.125* 6.71† – 2.54† – 1.85† – 9.28† – 2.22† – 2.09† – 373 6.61* 6.61* 2.44* 2.41* 1.72* 1.88* 9.15* 9.32* 2.23* 2.19* 2.210* 2.12* 6.66† – 2.52† – 1.83† – 9.20† 9.42† 2.22† 2.20† 2.07† 2.07† 398 6.57* 6.57* 2.41* 2.39* 1.69* 1.84* 9.01* 9.03* 2.22* 2.197* 2.09* 2.1* 6.61† – 2.50† – 1.79† – 9.10† – 2.21† – 2.06† – 423 6.51* 6.51* 2.38* 2.37* 1.66* 1.78* 8.78* 8.80* 2.22* 2.186* 2.085* 2.09* 6.55† – 2.47† – 1.76† – 8.97† – 2.21† – 2.04† – 448 6.36* 6.36* 2.34* 2.34* 1.57* 1.73* 8.84* 8.62* 2.21* 2.173* 2.07* 2.08* 6.34† – 2.41† – 1.67† – 8.73† – 2.20† – 2.01† – 473 6.50* 6.50* – 2.40* – 1.76* – 9.01* 2.20* 2.163* – 2.07* 6.52† – – – – – – 9.06† – 2.167† – 2.00† 513 6.49* 6.49* – 2.44* – 1.64* – 8.98* 2.20* 2.151* – 2.05* 6.50† – – – – – – 8.98† – 2.15† – 1.99† * Present experimental results † Barsch et al. results [21] Table( 3): Dielectric constants ε33 (calculated from data of Cross and Cline [17] and piezoelectric constants e (calculated from data for d31 of Yamada et al. [14]) by using the assumption (e = e31 = e33) versus temperature. T (K) Dielectric constants (ε33) Piezoelectric constants (e) (C.m–2) 298 40 0.690 323 44 0.764 348 50 0.842 373 61 0.941 398 78 1.099 423 133 1.432 448 2100 5.903 Physics - 211 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Fig. (1): Experimental results of elastic constants for lead germanate (Pb5Ge3O11) as a function of temperature, where (closed circles ••••●••••) represents the present experimental results of stiffened elastic constants (C´ ignoring piezoelectric stiffening) and (closed triangles (• –▲– •) represents present experimental results of unstiffened elastic constants (CE after subtracting piezoelectric stiffening) compared with Barsch et a. results [21] for which the solid lines is the stiffened elastic constants (C´) and the dashed lines is unstiffened elastic constants (CE). Physics - 212 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 السلوك المرن لجيرمانيت الرصاص بالُقْرب من درجِة حرارة اإلنتقال ِ اكرام جميل عبد الغني جامعة بغداد ،ابن الهيثم -كلية التربية ،قسم الفيزياء 2012كانون االول 9قبل البحث في : 2012نيسان 15استلم البحث في : الخالصة قياس جميع ثوابت المرونة الُمَصلَّبة وغيرالُمَصلَّبة لبلورة جيرمانيت الرصاص األحادية بدرجات حرارة تتراوح من التصحيح لعوامل استخدم بإستخدام تقنية التراكب النبضَي فوق الصوتي.وقد 513K الى 298K ةدرجة حرارة الغرف وقد بينت بعد طرحها من ثوابت المرونة الُمَصلَّبة وذلك لحساب ثوابت المرونة غيرالُمَصلَّبة. التصلب الكهروضغطية بزَيْاَدة درجِة الحرارة. تتناقص )C11, C33, C12, C13, C44 and C66(معامالت المرونة لجيرمانيت الرصاص النتائج ان ) اال K450من انخفاض شديد عند درجة حرارة اإلنتقاِل ( C11, C33, C12 and C13 اآلتية تعاني معامالت المرونة اذ وذلك بسبب كون K 473 و 453K انها تزداد بزَيْاَدة درجِة الحرارة مباشرة فوق درجِة حرارة اإلنتقال (كيوري) بين K473بين )يزدادقليال C12عدا ( ثم تتناقص بشكل طفيفمعامالِت درجِة الحرارة ضمن هذا المدى تكون موجبة ي K513و فإنه يزداد بصورة تدريجية بطيئة الى نقطة االنتقال وبعدها يبدأ بالتناقص الضئيل C44.اما ثابت المرونة القصَّ نتائج هذا البحث قورنتيتناقص تدريجيا وباستمرار مع زَيْاَدة درجِة الحرارة.فانه C66التدريجي. اما ثابت المرونة القصي مع النتائج العملية للبحوث المنشورة سابقا. .يرمانيت الرصاص ، المرونة، درجِة حرارة اإلنتقال ، النشاط البصري، البلورة الكهروضغطيةجالكلمات المفتاحية: